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Fixed points and orbits in skew polynomial rings.
- Source :
-
Journal of Algebra & Its Applications . Jul2024, Vol. 23 Issue 8, p1-9. 9p. - Publication Year :
- 2024
-
Abstract
- In this paper, we study orbits and fixed points of polynomials in a general skew polynomial ring D [ x , σ , δ ]. We extend results of the first author and Vishkautsan on polynomial dynamics in D [ x ]. In particular, we show that if a ∈ D and f ∈ D [ x , σ , δ ] satisfy f (a) = a , then f ∘ n (a) = a for every formal power of f. More generally, we give a sufficient condition for a point a to be r -periodic with respect to a polynomial f. Our proofs build upon foundational results on skew polynomial rings due to Lam and Leroy. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02194988
- Volume :
- 23
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra & Its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 178020456
- Full Text :
- https://doi.org/10.1142/S0219498824500786